# Definition of strictly convex preference

Let $$x,y\in X$$.

Does strictly convex preference (which implies that the utility is strictly quasiconcave) mean that:

$$x\succsim y$$ implies $$\alpha x+(1-\alpha)y\succ y$$ for any $$\alpha\in (0,1)$$?

• yes, if you add the assumption that $x \ne y$.
– tdm
May 2 '21 at 9:33